Page  00000053 Use of physical-model synthesis for developing experimental techniques in ethnomusicology- The case of the Ouldeme flute Patricio de la Cuadra', Christophe Vergez2, Rene Causse3 IRCAM 1 place Igor Stravinsky, 75004 Paris, France email:vergez2, rene.causse Center for Computer Research in Music and Acoustics Department of Music, Stanford University Stanford, California 94305-8180 USA pdelac1 Abstract As part of a collaboration project with ethnomusicologists and the Acoustique instrumentale group at IRCAM, we have studied and implement a physical model offlue instrument. The model has been investigated regarding its flexibility to geometry changes in the instrument, possibilities of timbre control as well as playability of the model. Two implementations have been developed: a C++ object using STK library and an external object for MAX/MSP Implementations have been designed allowing the user to adjust many parameters in real time and evaluate the response of the model. Also a maximum-likelihood algorithm has been implemented to automatically adjust the parameters of the model to a desire timbre. Finally a real-time MIDI controller has been built to control the model. Our goal is to study the musical scales of the flutes played by a tribe from North Cameroon: the Ouldeme. Each musician normally plays two flutes while and also sings a melody while inhaling. A band is usually formed by five players producing complex melodic and rhythmical textures. The flutes don't have toneholes and they are made of bamboo cane with a blowing end at one side and a close end at the other These flutes operate with a turbulent jet flow The behavior of this type of jet is less understood than the laminar one (case of recorder like instruments) and it is currently being studied in a parallel project. A one dimensional representation of the dynamics of the jet (formation, velocity fluctuation, oscillations) is used as described in Verge (1995). The bore is modeled using one dimensional waveguides. Visco-thermic losses and radiation of the sound are implemented as linear filters. 1 Introduction This work has begun within the framework of a project associating ethnomusicologists, psychoacous ticians and acousticians. The aim was to better understand musical scales used by Ouldeme flutist from North Cameroon (Fernando 2000). Ouldeme culture is essentially oral, and the concept of musical analysis doesn't exist, so that experiments with musicians are essential to better understand the underlying musical structure, including musical scales and more precisely the tunning strategy. 1.1 Ouldeme Flute I I Figure 1: Ouldeme flutists. A typical female flute band involves four or five women, each one playing two flutes. The flute is a piece of cylindrical bamboo closed at one end, similar to the Latin American pan pipes or zampon~as. There is no particular cut for the mouthpiece. Placing the tongue outside of his mouth, the player shapes the air stream, which then strikes a sharp edge of the cane, as shown in figure 1. Before playing the inside of the flute is moistened creating a thin film of water. It seems rea 53

Page  00000054 sonable to suppose that this prevents air leakage and, at a lower degree, adjusts the tuning of the instrument. The length of each flute is chosen to match the desired playing frequency. Fine tuning is of crucial importance and each player spends a lot of time choosing the right flute among a lot of nearly similar ones. 1.2 Experimental protocol From preliminary experiments carried out by ethnomusicologists, it was not possible to find a precise strategy concerning the tuning since no reliable scale could be extracted from successive frequency measurements. The idea of ethnomusicologists was then to use synthesis models of flutes, with precisely adjustable pitch so that they could both record player's pitch adjustment and test their reaction to an imposed detuning, in the spirit of the work done for xylophones from Central Africa (Arom and Voisin 1998). Within this scope, we proposed to build a physical model of the Ouldeme flute to use for time domain sound synthesis. In order to avoid to changing too much of the Ouldeme player's habits, it was decided to make them control physical models through gestural interfaces very close to real Ouldeme flutes and provide a synthesized sound as closed as possible to the real one. The Ouldeme flute physical model has been adapted from the M.P. Verge recorder model (Verge, Hirschberg, and Causse 1997). The main difference, other than the geometry, is that the air jet entering the bamboo pipe is turbulent. In spite of this basic difference, the two instruments present enough similarities that allow us to obtain good sound results using a laminar jet model. The physical model is briefly described in section 2.1 and 2.2 of the present article. Then, we focus on the real-time implementation of the model in section 2.3 and timbre adjustment of the model in section 2.4. The design of a dedicated MIDI control interface is described in section 3. 2 Modeling 2.1 Flue instruments functioning Flue instruments, like other sustained musical instruments, can be described as an excitation coupled to a resonator. The excitation consists of an intrinsically unstable jet which is directed toward a sharp edge, known as labium. On its path, the jet is submitted to the transverse acoustic field of the resonator. The two parts mutually affect each other. Pressure waves in the resonator perturb the jet causing it to inject flow periodically into the resonator. The jet then acts as an amplifier transfering its energy to the waves. This principle is common to most flue instruments (figure 2), with geometric variations which determine different operating conditions, such as the jet speed and a) --li Figure 2: Flute like instrument share a similar geometry. a)Recorder or organ b)Ouldeme flute the magnitude of the acoustic pressure. The speed of the jet, driven by the pressure difference, determines whether the jet will be laminar or turbulent. Turbulent jets are more complex than the laminar ones and there doesn't exist a simple and efficient model to use yet. The first step of this project consisted in an experimental study of a turbulent jet submitted to transverse perturbations (the jet at the output of an artificial mouth emerges in a transverse loudspeaker-induced pressure field). The resulting model is described in a companion paper ( Causse et al. (2002)). 2.2 The model The resonator is modelled by a one dimensional waveguide (Smith 1992) using fractional delay lines (Hinninen and Vilimiiki 1996) to allow continuous pitch control. Low-pass digital filters are used to describe radiation and visco-thermal losses in the bore. For the excitation, the following lumped elements are included: 1. Jet-labium interaction, including the contribution of the acoustic field from the pipe, the direct hydrodynammic feedback from the edge of the labium, the amplification of the perturbations in the jet and its convection toward the labium. 2. Vortex shedding at the labium is believed to be responsible for the major non-linear amplitude limiting mechanism of the pressure in the bore as well as the generation of high harmonics in the spectra (Fabre 1992). 3. Turbulent noise is added by filtering white noise and scaling it by a constant proportional to the jet velocity. These elements are mapped into a one dimensional representation of the dynamics of the jet which includes the formation, velocity fluctuation, oscillations as described in Verge (1995). 2.3 Implementation A flute physical model (Verge 1995) has been ported to MAX/MSP and STK (Cook and Scavone 2000); two 54

Page  00000055 platforms that allow real time control. The implementation has been designed in the spirit of a laboratory; allowing interactive control over a set of relevant parameters. The model is driven by the input pressure while the timbre of the sound can be adjusted by modifying the values of an adequate set of parameters: - Jet traveling distance before reaching the labium - Jet position with respect to the labium - Coupling gain; incidence of the jet injection over acoustic waves - Vortex amplitude; damping effect caused by vortex shedding at the labium - Cutoff frequency of visco-thermic losses filter - Turbulent noise gain To get synthesized sound as closed as possible to natural sounds, a procedure has been developed to automatically select the best values for the parameters: 2.4 Adjusting parameters of the model The geometry of the model has been set according to the geometry of the ould~m6 flute. A cost function measuring the similarity of the synthesized sound with respect to a desire sound has been defined. Finding good features to describe the timbre of the sound is a complex task that is beyond the scope of this paper. Instead, we look for simple mathematical features that will guide our search for finding a perceptible good approximation to a desire sound. We narrowed our search to the harmonic content of the steady state signal. A frequency domain analysis has been chosen, comparing the spectral distribution of energy and spectrum centroid and assigning a similarity evaluation to every sound candidate. The transient as well as the time domain envelope are very important for our perception of timbre, they will be controlled by the input of the model, the measured breath pressure. This operation produces a multidimensional function with a shape that is not known a priori. That makes it difficult to find an efficient algorithm to determine the maximum. The function could have an arbitrary shape and therefore there might be many local maximums. For each parameter we've chosen a bounded domain of values, as well as discrete steps to move from one value to the next one. To assure that a global maximum is found we explore the complete surface of the function, by evaluating all possible combinations of parameters. I -~~~~~~~~l:~P~~~:-::::::::::::::_:::,::::,::::::,,::,, I Figure 3: System complete; Synthetic flute with sensors. 3 Controlling In order to create a realistic performance situation, a cylindrical device has been built keeping the dimensions of the original flutes. A differential pressure sensor has been inserted close to the embouchure of the flute to assure short delays in the response of the instrument. The blow is directed toward one edge of the flute as shown in figure 2b, therefore the sensor was located near the upper side of the bore. It was necessary to create a conic shape to conduct the maximum amount of flow into the sensor. Analog amplification and low-pass filtering was used to create an envelope of the pressure signal. Another controller was designed to adjust the pitch of the synthesized sound. Two buttons have been inserted in the bore of the flute allowing the performer to raise or lower the pitch. Signals are then feed into an analog-to-midi interface (Fl~ty 2001) giving MIDI inputs for the input pressure and pitch of the model. The complete system is shown in figure 3 4 Summary A new application of real-time flute physical modelling has been described. An ethnomusicologist study regarding the tunning strategy of the Ould~m6 flutists has been assisted by the use of synthesized sounds and MIDI controllers. One important feature of physical model is their flexibility and their ability to produce new sounds by changing its parameters. This feature 55

Page  00000056 has been studied in our model, proposing a strategy of choosing these parameter to achieve a desire sound. Efficient real time implementations of a flute model have been coded allowing the use of up to ten instantiations of flutes with MIDI controllers simultaneously using MAX/MSP in a Macintosh PowerBook G4. 5 Acknowledgment Part of this work has been funded by Program Cognitique from the French Research Ministry. References Arom, S. and F. Voisin (1998). Theory and technology in african music. In The Garland Encyclopaedia of World Music 2: Africa, New-York, Garland. in Ruth Stone (ed.). Causse, R., C. Vergez, B. Fabre, and C. Segoufin (2002). Use of physical model synthesis for developing experimental investigation techniques in ethnomusicology; the case of the ouldm flute. Forum Acusticum, Sevilla 1(1). Cook, P. and G. Scavone (2000). The synthesis toolkit (stk). URL: Fabre, B. (1992). La production de son dans les instruments a embouchure de fltte: moddle aeroacoustique pour la simulation temporelle. Le Mans, France: These de doctorat, Universite de Maine. Fernando, N. (2000). A propos de statut de l'octave dans un systeme pentatonique du nord camerun. Musicae Scientiae, European Society for the Cognitive Sciences of Music 1(1), 83-95. Flety, E. (2001). Atomic pro: "a multiple sensor acquisition device. NIME, Dublin. Hiinninen, R. and V. Valimaki (1996). An improved digital waveguide model of a flute with fractional delay filters. Proc. Nordic Acoustical Meeting (NAM'96) 1(1), 437-444. Smith, J. (1992). Physical modeling using digital waveguides. Computer Music Journal 4(16), 74-87. Verge, M. (1995). Aeroacoustics of Confined Jets. The Netherlands: PhD. thesis, Eindhoven University of Technology. Verge, M., A. Hirschberg, and R. Causs6 (1997). Sound production in recordelike instruments. ii. a simulation model. J. Acoust. Soc. Am 5(101), 2925-2939. 56